If a bus driver leaves her first stop by 7:00 a.m., her route will take less than 37 minutes. If she leaves after 7:00 a.m., she estimates that the same route will take no less than 42 minutes. Which inequality represents the time it takes to drive the route, [tex]$r$[/tex]?
A. [tex]$r\ \textless \ 37$[/tex] or [tex]$r \geq 42$[/tex]
B. [tex]$r\ \textless \ 37$[/tex] or [tex]$r\ \textgreater \ 42$[/tex]
C. [tex]$37\ \textless \ r \geq 42$[/tex]
D. [tex]$37\ \textgreater \ r \geq 42$[/tex]
Answer (2)
Express the first condition as an inequality: r < 37 .
Express the second condition as an inequality: r ≥ 42 .
Combine the two inequalities with 'or' since either condition can be true: r < 37 or r ≥ 42 .
The inequality representing the time it takes to drive the route is: r < 37 or r ≥ 42
Explanation
Problem Analysis Let's analyze the given information to determine the inequality that represents the time it takes to drive the route, denoted by r .
First Condition The problem states that if the bus driver leaves by 7:00 a.m., the route takes less than 37 minutes. This can be written as the inequality: r < 37
Second Condition The problem also states that if the bus driver leaves after 7:00 a.m., the route takes no less than 42 minutes. This can be written as the inequality: = 42"> r " >= 42
Combining the Inequalities Since either the first condition or the second condition can be true, we combine the two inequalities using 'or'. Therefore, the inequality that represents the time it takes to drive the route is: r < 37 or r ≥ 42
Final Answer The correct inequality that represents the time it takes to drive the route is r < 37 or = 42"> r " >= 42 .
Examples
Understanding inequalities is crucial in many real-world scenarios. For instance, consider a delivery service that guarantees delivery within a certain time frame. If a package is sent before a specific cutoff time, the delivery time is less than 24 hours. If sent after the cutoff, the delivery time is no less than 48 hours. This situation can be represented using inequalities, similar to the bus route problem. Inequalities help set expectations and manage customer satisfaction by providing a clear range of possible outcomes.
The inequality representing the time it takes to drive the route is r < 37 or r ≥ 42 . This demonstrates that if the driver leaves at 7:00 a.m., the drive takes under 37 minutes, and if leaving later, it takes 42 minutes or more. Thus, the answer is option A.
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